Calcium Regulation of an Actin Spring
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Citation
Tam, Barney K., Jennifer H. Shin, Emily Pfeiffer, P. Matsudaira,
and L. Mahadevan. “Calcium Regulation of an Actin Spring.”
Biophysical Journal 97, no. 4 (August 2009): 1125–1129. © 2009
Biophysical Society
As Published
http://dx.doi.org/10.1016/j.bpj.2009.02.069
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Elsevier
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Fri May 27 00:58:48 EDT 2016
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http://hdl.handle.net/1721.1/96169
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Biophysical Journal Volume 97 August 2009 1125–1129
1125
Calcium Regulation of an Actin Spring
Barney K. Tam,†{ Jennifer H. Shin,k Emily Pfeiffer,‡ P. Matsudaira,‡§{ and L. Mahadevan††‡‡*
†
Department of Physics, ‡Department of Biological Engineering, and §Department of Biology, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139; {Whitehead Institute for Biomedical Research, Cambridge, Massachusetts 02142; kDepartment of Bio and
Brain Engineering, and Department of Mechanical Engineering, KAIST, Daejeon, 305-701, Republic of Korea; ††School of Engineering and
Applied Sciences, and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138;
and ‡‡Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115
ABSTRACT Calcium is essential for many biological processes involved in cellular motility. However, the pathway by which
calcium influences motility, in processes such as muscle contraction and neuronal growth, is often indirect and complex. We
establish a simple and direct mechanochemical link that shows how calcium quantitatively regulates the dynamics of a primitive
motile system, the actin-based acrosomal bundle of horseshoe crab sperm. The extension of this bundle requires the continuous
presence of external calcium. Furthermore, the extension rate increases with calcium concentration, but at a given concentration,
we find that the volumetric rate of extension is constant. Our experiments and theory suggest that calcium sequentially binds to
calmodulin molecules decorating the actin filaments. This binding leads to a collective wave of untwisting of the actin filaments
that drives bundle extension.
INTRODUCTION
Calcium regulates the dynamics of many motile cellular
processes. For example, calcium binding to the protein
troponin C (1) mediates muscle contraction, whereas calcium
concentration gradients (2) regulate neurite growth cone elongation. In Vorticella, calcium plays a direct role in neutralizing a charged polyeletrolyte gel that on contraction drives
movement (3). In each of these systems, the mechanics of
motility are coupled to the chemistry of calcium binding.
Understanding this often complex coupling is an important
problem in biology.
In this study, we establish a simple and direct mechanochemical link that shows how calcium quantitatively regulates
the dynamics of a primitive motile system, the actin-based
acrosomal process of the Limulus sperm. The acrosomal reaction of these cells is an example of micron-scale movement
occurring in short (~10 s) timescales. During fertilization,
a 60-mm long bundle of actin filaments, originally coiled within
the cell (Fig. 1 A), straightens and extends to puncture protective layers covering the egg (4). This actin bundle is crystalline
and tapered with a tip consisting of ~15 filaments, and a base of
~80 filaments (5). Each actin monomer is decorated in a 1:1
fashion by a scruin-calmodulin complex and neighboring filaments are bound to each other by scruin-scruin interactions
(6,7). Scruin initially locks the actin filaments into a slightly
overtwisted coiled superhelical bundled state, whereas
calmodulin (CaM) confers calcium-sensitivity. On binding of
calcium to CaM, the scruin-CaM complex unlatches, causing
the filament—and hence bundle—overtwist to relax and drive
the extension of this actin spring into the straight true discharge
Submitted June 23, 2008, and accepted for publication February 24, 2009.
*Correspondence: lm@seas.harvard.edu
P. Matsudaira’s present address is Department of Biological Sciences,
National University of Singapore, Singapore 117543.
Editor: Herbert Levine.
2009 by the Biophysical Society
0006-3495/09/08/1125/5 $2.00
(TD) state (6,8). Though the presence of external calcium is
required for the reaction to occur, no quantitative experiments
have investigated the role of calcium in the reaction. Specifically, it remains unclear whether calcium is required only to
initiate the reaction, with the subsequent extension proceeding
independently of calcium or if calcium is continuously
required during the extension. To address this issue and probe
the effects of external calcium on the dynamics of the TD
extension, we use laser irradiation to trigger the TD reaction
in a controlled environment, and use fluorescence to image
calcium during the reaction.
MATERIALS AND METHODS
Sperm cells were collected from male crabs and washed in artificial sea
water (ASW: 423 mM NaCl, 9 mM KCl, 9.27 mM CaCl2, 22.94 mM
MgCl2, 25.5 mM MgSO4, 2.15 mM NaHCO3, 10 mM Tris, pH adjusted to
7.9–8.0) twice. The sample was then diluted 1:1000 with ASW and flowed
into a flow chambers constructed from coverslips and double-sided adhesive
tape to conduct the experiments. To immobilize the cells, the bottom coverslip
was first treated with a 2% (v/v in acetone) BIOBOND nonspecific adhesive
solution (BBInternational Inc., Cardiff, UK) and then rinsed with water.
An EGTA solution was prepared by substituting 0.1 mM EGTA for
9.27 mM CaCl2 to chelate residual Ca2þ ions. Solutions for the calcium titration experiments were made by dissolving additional amounts of CaCl2 to
ASW as required to achieve desired calcium concentrations.
All experiments were carried out at room temperature with a Nikon TE-3000
inverted microscope with a NA 1.4 100 oil-immersion objective. A laser
tweezer-like setup was installed with a 532-nm 25 mW laser from World
Star Tech (Toronto, Ontario, Canada) to activate the cells. Video was recorded
with a Dage MTI CCD100 camera, and digitized for tracking with a PC. Individual extension profiles were visually tracked using software provided by
Photron Cameras (San Diego, CA).
RESULTS AND DISCUSSION
To find out if calcium is continuously required for the acrosomal reaction to proceed, we first trigger the TD reaction in
ASW containing 9 mM CaCl2 and simultaneously monitor
doi: 10.1016/j.bpj.2009.02.069
1126
Tam et al.
FIGURE 1 (A) Schematic of Limulus
sperm cell. Note the gradual tapering
of the bundle from the tip to the base
(16–80 filaments), as well as the polygonal nature of the bundle itself. The
region where a transition between the
TD and coil occurs has a high degree
of curvature in addition to a nonzero
twist gradient, providing a possible location where calcium can preferentially
bind to calmodulin. (B) Extension profile
for multiple cells undergoing acrosome
reaction. Arrows mark approximate introduction of EGTA, and at a later time, calcium-rich ASW. EGTA chelates calcium arresting the acrosome reaction.
Reintroducing calcium restarts the extension. Such behavior is consistent with a reaction mechanism involving sequential binding of calcium to a local region
on the bundle. (C) Effect of calcium on TD Extension. The average velocity of the TD extension increases at higher calcium concentrations. Each point averages
over between 6 and 10 experiments.
the extension. As the actin bundle extends, we flow in a solution
of zero-Ca2þ ASW with 0.1 mM EGTA, a calcium chelating
agent that eliminates calcium. This has the effect of arresting
all motion within one second (Fig. 1 A). Reintroducing regular
ASW to the flow chamber 30 s later results in a resumption of
the extension, although with a lower velocity (Fig. 1 B).
FIGURE 2 Series of calcium titration experiments
measuring the TD extension. (A) The length of the bundle
extends at an increasing rate as a function of calcium
concentration but the trajectories exhibit significant
nonlinear behavior at long times. (B) When the volume of
the tapered bundle that is extended is plotted as a function
of time, this nonlinearity is essentially eliminated for higher
values of calcium concentration. However, for the low
calcium (5, 10 mM) the nonlinearity and high variance
data suggest stochastic binding behavior during CaM-Ca2þ
reaction.
Biophysical Journal 97(4) 1125–1129
Calcium Regulation of an Actin Spring
FIGURE 3 (A) Rate constant k calculated using a noncooperative,
constant rate CaM-Ca2þ binding mechanism. The slight dependence on
[Ca2þ] suggests a deviation from the mechanism due to an overestimation
of [CaM] participating in the reaction. (B) Normalized volume extension
rates. Values were calculated from least-squares fitting of volumetric extension profiles as functions of time. The linear behavior (dashed line) suggests
a rate mechanism involving calmodulin with one calcium binding site.
As a control, we carried out a second series of experiments
reversing the order of solutions added. Instead of ASW with
calcium, we initially exposed the cells to zero-Ca2þ ASW
solution and then irradiated the sperm with a laser. We find
that the TD was never triggered in these experiments.
However, when we replace the zero-Ca2þ solution with ASW
within 15–20 s of laser irradiation, we are able to trigger the
TD extension. Reintroducing ASW after a period >15–20 s
does not produce TD extension. This probably occurs because
although the laser induces depolarization of the membrane
leading to the opening of voltage dependent calcium channels, its effect lasts only for a short time, after which the
membrane becomes repolarized. Taken together, these experiments prove that the TD reaction proceeds only while the cell
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is in calcium-rich ASW, eliminating the possible scenario
where Ca2þ only initially triggers the extension, which then
proceeds in a self-sustained manner. Moreover, the subsequent extension observed when calcium-rich ASW is reintroduced suggests that even though there is an abundance of
calcium everywhere around the bundle (9), a localized
untwisting mechanism generates motion, i.e., there is a localized front of filament and bundle untwisting along the bundle
that propagates along it leading to extension.
To quantify the effect of external calcium concentrations on
the dynamics of extension, we titrate the calcium concentrations in modified ASW to vary from 5 to 50 mM. In each solution of ASW, we trigger the acrosome reaction in different
sperm cells, for a total of 6–10 sample extension profiles per
concentration. Our results show that i), the velocity of extension increases as a function of calcium concentration
(Fig. 1 C), and ii), the trajectories of all extensions exhibit
significant nonlinear behavior (Fig. 2 A) at large extensions.
The extension profiles of individual cells as a function of
time show that the velocity of extension is not constant–it is
initially large but decreases before the bundle is fully
extended. To understand this, we begin with the simple fact
that the bundle is tapered (3), so that the amount of actin,
scruin, and calmodulin that are present in a stoichiometric
ratio 1:1:1 varies with location along the bundle. Thus, consistent with a local mechanism for filament untwisting, the
number of calmodulins available for binding is a function
of the location and thus the length of the bundle that has
untwisted. To quantify this dependence, we note that the
volume
R L of a tapered bundle of length L is given by
V ¼ 0 pr2 dl, where the radius r ¼ cl þ r0. Integration yields
3
VðLÞ ¼ pðc2 L3 þ cr0 L2 þ r02 LÞ; where c ¼ 7.4 104 and
r0 ¼ 24 nm (10). Volume is hence a nonlinear function of
the length, L ˛ [0,60] mm. When we recast the bundle extension in terms of the volume extended as a function of time
(Fig. 2 B), we find that the volume of the bundle extruded
varies linearly with time. Moreover, the rate of this volume
extension is dependent on the external calcium concentration,
at least for low concentrations, but eventually saturates.
These observations can be understood by considering the
binding of Ca2þ to the scruin-CaM complex, given by the
following reaction mechanism:
k
CaM þ Ca2 þ / CaM$Ca2 þ :
(1)
Here, k is an effective rate constant with units of [M1 s1],
which governs the binding of Ca2þ to the scruin-CaM
complex associated with the twisted filaments. We assume
that unbinding occurs rarely so that we neglect its contribution
to the kinetics. The local calcium concentration within the
cell, [Ca2þ], is essentially constant. This assumption is
reasonable given that diffusion occurs on the order of milliseconds for a typical cellular dimension of 1 mm and a free
diffusion coefficient D ¼ 140–300 mm2/s for calcium ions
in solution. We do not consider any Ca2þ-sequestering organelles or buffers (11,12). The concentration of calmodulin
Biophysical Journal 97(4) 1125–1129
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Tam et al.
FIGURE 4 Entrance region of the
nucleus before (A) and during (B) the
extension. As evidenced in the electron
micrographs, the bundle situated in the
channel features an untwisted parallel
array of filaments. This characteristic is
typical of the true discharge bundle,
whereas the part of the bundle entering
into the channel is locally bent and
twisted and exhibits slippage with
respect to neighboring filaments (Scale
bar, 100 nm). Filaments in the coil are
twisted over each other at a regular
interval and also have regularly spaced
kinks (3). (C) Evidence for calcium
localization during the acrosomal reaction. Selected frames showing calcium
fluorescence from 2D time-lapse confocal microscopy using 7.7 mM of the
AM-ester form of calcium green 1 for
labeling. Image shown in (a) is a DIC
image of an unreacted cell, (b) before,
and (c, d, and e) 42, 47, and 50 s after
the introduction of a calcium ion carrier
(A23187) into the flow chamber. Once
the ionophore is introduced into the
flow chamber, a bright spot appears in
the middle of the cell before the extension of the acrosome. (D) Images were
captured immediately after calcium
ionophore was added in the channel.
Before the reaction begins (from 0 s to
18.1 s), calcium resides predominantly
inside the cytoplasm at the base of the
nucleus. A bright spot indicated by the
arrowhead in the middle of the sperm
head is also observed. As the extension
begins (~after 10 s), this spot brightens
briefly then disappears, whereas the
extending bundle is brightly labeled
with calcium dye indicating the association of calcium to the actin bundle. The
bright spot, found in half of the collected
data, is consistent with the presence of
a localized region of calcium near the
entrance region of the nuclear channel
before extension. The extinction of this
spot may be associated with the slight
twitching of the sperm head typically
observed during the bursting of the
acrosomal vesicle at the beginning of
extension.
participating in the reaction is constant for a given region and
can be equated to the number density, n, of CaM in the bundle.
To calculate this density, we again appeal to the bundle geometry. Because the helical pitch between adjacent actin monomers in the axial direction is 2.7 nm (3), 1 mm of this filament
contains ~370 actin/scruin/CaM complexes. Because the 60mm bundle tapers from 80 to 20 filaments, having an average
50 filaments, we calculate the total number of CaM to be
~1.13 106 (10). Using a total bundle volume, Vtot, of 2.0 1019 m3, calculated based on the measured dimensions of
Biophysical Journal 97(4) 1125–1129
a truncated cone (upper base radius, 10 nm; lower base radius,
50 nm; height, 60 mm), we thus find the number density n to be
~0.5 1025 CaM mol/m3, or equivalently, 8 103 M. On
calcium binding, the CaM $ Ca2þ complex allows the strained
actin filaments to untwist, hence extending the kinked twisted
bundle. The rate equation that quantifies this simple binding
mechanism is
d CaM$Ca2 þ
d½CaMðLÞ
¼ kn Ca2 þ : (2)
¼ dt
dt
Calcium Regulation of an Actin Spring
Given a constant [Ca2þ], Eq. 2 trivially yields [CaM $ Ca2þ] ¼
kn[Ca2þ]t. Because CaM $ Ca2þ can only form on the bundle,
the total number of complexes is [CaM $ Ca2þ]Vtot. However,
the total number of CaM $ Ca2þ complexes associated with
a given volume, V(L) of the extending bundle is [CaM]V(L).
These two quantities are equal to each other because the
extension is a direct result of CaM $ Ca2þ formation. This
equality relates the kinetics associated with the Ca2þ-CaM
reaction mechanism to the trajectories in Fig. 2 B for the
volumetric extension rate. By identifying V(L)/Vtot ¼
knt[Ca2þ]/[CaM] as the effective volumetric reaction rate,
and determining the rate constant, k, we find that it is independent of calcium concentration (Fig. 3 A), consistent with
a single-site binding mechanism. Moreover, this binding
rate is comparable to rate constants observed in other calcium
binding systems (13,14).
Although a noncooperative two-site binding framework
was used previously to analyze in vitro calorimetric experiments (9), our in vivo results suggest that CaM conformational change occurs with the binding of a single calcium
ion. Purified bundles of actin, scruin, and CaM will most
likely behave differently than bundles in a living cell.
Conformation changes for the bundle in our experiments
occur dynamically, far away from binding equilibrium,
unlike the calorimetric experiments. Indeed, a characteristic
rate of conformational change for CaM associated with the
effective rate constant k ¼ 4 M1s1 (Fig. 3 A) can be calculated by multiplying k by the saturating Ca2þ concentration
of ~50 mM, yielding a value of 0.2 s1. This value is significantly less than the observed closed / open rate of 2.7 104 s1 for CaM conformational changes (15), suggesting
that calcium binding is not the rate-limiting step of the reaction. Instead, local rearrangements of the actin filaments as
they slide relative to each other during untwisting are
a much more likely candidate limiting the rate of extension.
Such a mechanism can arise from the densely packed filamentous bundle, where the untwisting motions driven by
calcium binding will lead to large local shear rates. In addition, this sequential binding mechanism suggests that the
highly strained transition region characterizing the TD-coil
interface as it bends/twists into the nuclear channel is where
calcium ions preferentially bind to CaM. This follows
because a highly strained region allows significantly greater
access to the Ca2þ binding sites of CaM, hence facilitating
the reaction and increasing the rate of calcium binding
locally. Indeed, in Fig. 4, A and B, we show electron micrographs consistent with this structural transition region of the
bundle near the entrance to the nuclear channel.
To complement the kinetic measurements, we also used
calcium imaging via fluorescence to follow the acrosomal
reaction in time. In Fig. 4, C and D, we show the results of
2D time-lapse confocal microscopy to track the dynamics
of calcium introduced using an ionophore. We see that
before the reaction starts, the calcium resides inside the cytoplasm at the base of the nucleus. On activation however, the
1129
extending bundle is labeled with the calcium dye, which is
consistent with the association of calcium with the bundle.
In addition, a bright spot is observed in half of the images
near the entrance of the bundle into the channel (Fig. 4 A),
implying that calcium binds at a localized region.
Our experiments are consistent with a model that accommodates a sequential calmodulin-calcium binding mechanism and that presents a natural region within the bundle
wherein the reaction occurs. Knowledge of how calcium
binds to calmodulin (13), and of the structural transformations of the actin bundle (16) provides us with a biophysical
basis that combines structural and dynamical information to
show the mechanochemistry of a simple actin spring that
stores energy and, when activated, generates force (9,17)
to carry out a crucial physiological function.
This work was supported by the National Institutes of Health (P.M., L.M.).
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